Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1656$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,8,2,15,7)(3,13,5)(4,14,6)(11,12), (1,4,2,3)(5,12,16)(6,11,15)(7,9,13,8,10,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 8: $D_{4}$ 12: $A_4$, $C_6\times C_2$ 24: $A_4\times C_2$ x 3, $D_4 \times C_3$ 48: $C_2^2 \times A_4$ 96: $C_2^4:C_6$, 12T51 192: $C_2\wr A_4$ x 2, 12T87 384: 12T134, 16T716, 16T722 768: 32T34728 1536: 16T1299 3072: 24T5579 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $A_4$
Degree 8: $C_2\wr A_4$
Low degree siblings
16T1656 x 3, 16T1658 x 4, 32T397390 x 4, 32T397391 x 2, 32T397392 x 2, 32T397396 x 2, 32T397397 x 2, 32T397398 x 2, 32T397399 x 2, 32T397400 x 2, 32T397401 x 2, 32T397745 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 69 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6144=2^{11} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |